Related papers: Measuring maximal eigenvalue distribution of Wisha…
Repetition-rate-scanned lasers are practical in accordion frequency comb generation that serves as a variable gearbox connecting optical and radio wave domains. Rapid and wide-range scanned repetition rate can benefit versatile purposes,…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
We use free probability to compute the limiting spectral properties of the harmonic mean of $n$ i.i.d. Wishart random matrices $\mathbf{W}_i$ whose limiting aspect ratio is $\gamma \in (0,1)$ when $\mathbb{E}[\mathbf{W}_i] = \mathbf{I}$. We…
Rare-earth-doped fiber lasers are emerging as promising high-power mid-infrared sources for the 2.6-3.0 {\mu}m and 3.3-3.8 {\mu}m regions based on erbium and holmium ions. The intermediate wavelength range, however, remains vastly…
This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments.…
We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this…
Multidimensional optimization schemes for TW hard X-Ray free electron lasers are applied to the cases of transversely uniform and parabolic electron beam distributions and compared to examples of transversely Gaussian beams. The…
Let $X_N$ be a $N \times N$ real Wishart random matrix with aspect ratio $M/N$. The limit eigenvalue distribution of $X_N$ is the Marchenko-Pastur law with parameter $c = \lim_N M/N$. The limit moments $\{m_n\}_n$ are given by $m_n =…
Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…
The work was aimed to generate random laser emissions simultaneously at two wavelengths in a weakly scattering system containing mixture of binary dyes, rhodamine-B (Rh-B) and oxazine-170 (O-170) dispersed with ZnO nano-particles served as…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…
We have developed a Watt-level single-frequency tunable fiber laser in the 915-937 nm spectral window. The laser is based on a neodymium-doped fiber master oscillator power amplifier architecture, with two amplification stages using a 20 mW…
We report on a long wavelength emitting rare earth doped fiber laser with emission centered at 3.5 {\mu}m and tunable across 450 nm. The longest wavelength emission was 3.78 {\mu}m, which is the longest emission from a fiber laser operating…
Experimental configuration for investigating the dynamics and the statistics of the phase locking level of coupled lasers that have no common frequency is presented. The results reveal that the probability distribution of the phase locking…
An ultrafast laser based on coherent beam combination of four ytterbium-doped step-index fiber amplifiers is presented. The system delivers an average power of 3.5 kW and a pulse duration of 430 fs at 80 MHz repetition rate. The beam…
We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…
The top eigenvalues of rank $r$ spiked real Wishart matrices and additively perturbed Gaussian orthogonal ensembles are known to exhibit a phase transition in the large size limit. We show that they have limiting distributions for…
High power fiber lasers operating at the 1.5micron wavelength region have attractive features like eye-safety and atmospheric transparency, and cascaded Raman fiber lasers offer a convenient method to obtain high power sources at these…
Let $\mathbf{W}\in\mathbb{C}^{n\times n}$ be a {\it single-spiked} Wishart matrix in the class $\mathbf{W}\sim \mathcal{CW}_n(m,\mathbf{I}_n+ \theta \mathbf{v}\mathbf{v}^\dagger) $ with $m\geq n$, where $\mathbf{I}_n$ is the $n\times n$…